New York capitalized on the man-advantage, scoring four power-play goals on eight opportunities. The Islanders' Frans Nielsen and John Tavares each scored a pair of goals, while Kyle Okposo added one goal, and goaltender Evgeni Nabokov made 35 saves.
The loss snapped Boston's home winning streak at eight games and the Bruins are now 13-1-2 in their last 16 games at the Garden.
Krejci gave the Bruins an early 1-0 lead at 4:25 of the first period. It was his ninth of the season and the 100th of his career. He also extended his point streak to five games and has three goals and three assists during the stretch.
It appeared the Islanders had tied the game at 1-1 at 15:25 of the opening period, but the referee whistled the play dead during a scramble in front of Rask before the puck crossed the goal line.
New York tied it for real when Nielsen scored a power-play goal at 5:56 of the second period. Nielsen took a pass from Tavares and beat Rask, who was screened in front.
Boston responded with a pair of quick goals to gain a 3-1 advantage. Bergeron scored a power-play goal at 12:33, before Paille redirected a Zdeno Chara one-timer at 12:58 to give the Bruins a two-goal lead.
New York, however, responded.
Penalty issues cost the Bruins as the Islanders scored a pair of power-play goals late in the second period to tie the game at 3-3.
Nielsen scored his second of the night, another power-play tally, at 16:30, before Okposo scored with 2.6 seconds remaining in the period to tie it.
The Islanders kept their momentum going at the start of the third when Tavares scored only 32 seconds into the period. Tavares added his second of the game, a power-play goal at 13:17, to give New York a 5-3 advantage.
MILLER'S TIME: On Monday, the Bruins recalled defenseman Kevan Miller from Providence and he was in the lineup against the Islanders. It was his 10th game in the NHL, which means if the Bruins decide to assign him to Providence, he'll have to clear waivers. General manager Peter Chiarelli recently said the next time Miller is in Boston it would be for good. With fellow defenseman Dennis Seidenberg out for the remainder of the season with a torn MCL and ACL in his right knee, this could be Miller's opportunity to remain in the lineup. Once Dougie Hamilton (lower body) returns, Miller's presence will keep a healthy competition for the younger members of Boston's defensive corps.
JOHNSON BACK IN THE MIX: With Bruins forward Carl Soderberg has been experiencing symptoms of a concussion, he missed his second consecutive game. As a result, the Bruins early Tuesday morning recalled forward Nick Johnson from Providence. He was in the lineup against the Islanders and played alongside Ryan Spooner and Matt Fraser. That trio played together as a line for the P-Bruins earlier this season and had some success.
UP NEXT: The Bruins will host the Nashville Predators Thursday night (7 p.m.) at TD Garden.